When she was a teenager, her aunt took her and her cousin to cabarets to sing, but her father encouraged her to keep attending school, in hopes that she would become a Spanish language teacher. However, one of her teachers told her that as an entertainer she could earn in one day what most Cuban teachers earned in a month.
In 1960, in the aftermath of the Cuban Revolution, Cruz moved to the United States. In 1961, she and her orchestra began performing at the Hollywood Palladium. The following year, she married her lead trumpeter, Pedro Knight. In 1965, Cruz and her husband left the orchestra. She was by then a US citizen and never returned to Cuba.